Abstract
Turbulent thermal convection is characterized by the formation of large-scale structures and strong spatial inhomogeneity. This work addresses the relative heat transport contributions of the large-scale plume ejecting vs. plume impacting zones in turbulent Rayleigh-Bénard convection. Based on direct numerical simulations of the two dimensional (2-D) problem, we show the existence of a crossover in the wall heat transport from initially impacting dominated to ultimately ejecting dominated at . This is consistent with the trends observed in 3-D convection at lower Ra, and we therefore expect a similar crossover to also occur there. We identify the development of a turbulent mixing zone, connected to thermal plume emission, as the primary mechanism for the takeover. The mixing zone gradually extends vertically and horizontally, therefore becoming more and more dominant for the overall heat transfer.
Highlights
Turbulent thermal convection is characterized by the formation of large-scale structures and strong spatial inhomogeneity
Based on direct numerical simulations of the two dimensional (2-D) problem, we show the existence of a crossover in the wall heat transport from initially impacting dominated to ejecting dominated at Ra ≈ 3 × 1011
One of the advantages of the 2-D confined (Γ = 2) cell is that the configuration of the largescale circulation (LSC) is stable, which means that one can safely assume the number of the convection rolls to be fixed for all times
Summary
Crossover of the relative heat transport contributions of plume ejecting and impacting zones in turbulent Rayleigh-Benard convection(a). Assuming that the large-scale rolls are of similar size and always located at the same places, for very large Ra ≥ 1013 and in two-dimensional (2-D) direct numerical simulations, Zhu et al [24] obtain effective scaling laws: Nuloc ∼ Ra0.28 in the plume impacting region and Nuloc ∼ Ra0.38 in the plume ejecting region This implies that for very large Ra, the latter scaling wins for the overall (global) Nusselt number, N u ∼ Ra0.38. This analysis is relevant in the context of the findings of Zhu et al [24,27], who showed that beyond Ra ≥ 1013, both the local heat flux in the plume ejecting regions (which grows with increasing Ra) and the overall heat flux scale steeper than the classical Malkus scaling Nu ∼ Ra1/3 This reflects the onset of the ultimate regime around that Rayleigh number, consistent with theoretical predictions [13,28] and experimental measurements [29,30]. Crossover of the relative heat transport contributions in turbulent RBC (a) Impacting
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